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  4. On putting a capillary tube in a pot filled with water, the level of water rises upto a height of 4 cm in the tube. If a tube of half the diameter is used instead, the water will rise to a height of nearly

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Q. On putting a capillary tube in a pot filled with water, the level of water rises upto a height of $4\, cm$ in the tube. If a tube of half the diameter is used instead, the water will rise to a height of nearly

Mechanical Properties of Fluids

Solution:

For capillary tube
$h=\frac{2 T}{r \rho g}$
We can say
$h \propto \frac{1}{r} \text { or } h \propto \frac{1}{d}$
So, $\frac{h_{1}}{h_{2}}=\frac{d_{2}}{d_{1}}$
$\Rightarrow \frac{4}{x}=\frac{d}{2 d}$
$\Rightarrow x=8\, cm$